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The lightcurves of asteroids are essential for determining their physical characteristics, including shape, spin, size, and surface composition. However, most asteroids are missing some of these basic physical parameters due to lack of photometric data. Although a few telescopes or surveys are specially designed for photometric lightcurve observations of asteroids, many ground-based and space-based sky surveys for hunting new exoplanets, transient events, etc., should capture numerous small Solar system objects. This will benefit the physical studies of these objects. In order to extract data of these moving objects from time-domain photometric surveys, we have developed a new method using the model tree algorithm in the field of machine learning. A dedicated module is built to automatically identify moving objects in data set and extract their photometric and astrometric data. As the first application of this novel method, we have analysed data in five fields of the Yunnan-Hong Kong wide field photometric (YNHK) survey, from which 538 lightcurves of 211 asteroids are successfully extracted. Meanwhile, we also tested the method based on the data from NASA’s Transiting Exoplanet Survey Satellite, and the result proves the reliability of our method. With derived lightcurves of 13 asteroids from the YNHK survey, we have determined their synodic spin periods, among which the periods of four asteroids are estimated for the first time. In future, we are going to apply this method to search for small objects in the outer part of the Solar system from the Chinese Space Station Telescope survey.

The Deep Space Climate Observatory (DSCOVR) is located near the Lagrangian L1 point of the Earth. Their EPIC images indicate exceptionally large values of the Earth's planetary albedo in December 2020, having daily average surged above 0.320 for consecutive three weeks. Independent evaluation of the Earth’s albedo using a numerical weather prediction model (OpenIFS of ECMWF) suggests that this is an over-estimate. Given the difference between satellite-based and model-based albedo estimates, the reconstructed from images top-of-atmosphere short-wave radiosity is over-estimated. We suggest the discrepancy is explained by a weakness of short-wave angular distribution models (ADMs) based on Clouds and the Earth's Radiant Energy System’s The Tropical Rainfall Measuring Mission (CERES/TRMM) in full back-scattering geometry. This conclusion is supported by disk-integrated short-wave anisotropy factors in December 2020, estimated using CERES ADMs, being lower than measured by NIST Advanced Radiometer (NISTAR).

Polarimetry is a powerful technique to study the surfaces of Solar System objects, especially at small phase angles where the so-called the negative polarization branch (NPB) is observed. The NPB can have different shape and polarization values for different composition of the surfaces. For rocky surfaces, it has a parabolic shape with a minimum around 10° and inversion point (the angle where the polarization changes from negative to positive) around 20°. However, for icy surfaces (satellites of giant planets, cometary nuclei, and Trans-Neptunian objects), the NPB becomes very asymmetric, and its minimum shifts to smaller phase angles. The cause of this has been attributed to Coherent Backscattering Mechanism (CBM), which is known to be very sensitive to the size of particles and porosity of the medium. Recently, we have been able to accurately determine the NPB of jovian satellites Europa, Ganymede, and Io. The NPBs for Europa and Ganymede are very similar (despite the difference in their geometric albedo, 0.67 for Europa and 0.44 for Ganymede). Their NPBs appeared to be strongly shifted to small phase angles with a single narrow minimum (unlike a bimodal curve with a deep and narrow and broad and shallow overlapping NPBs as was suggested in Rosenbush et al. 2015). Io, unlike Ganymede and Europa, has a more extended, although still asymmetric, NPB, despite a similarity of Io’s albedo (0.63) to Europa’s albedo. As an example, we show the observed polarization phase curve for Europa (Fig. 1). Its NPB is evidently formed by CBM. To find the properties of the regolith particles, we accomplished computer modeling of the polarimetric curves using the radiative-transfer coherent-backscattering (RT-CB) method (e.g., Muinonen et al. 2015). The best fit for Europa, shown in Fig. 1, was achieved for a regolith layer of single-scattering albedo ~0.985 and extinction mean-free-path-length ~16 microns. We will also present the results for Io and Ganymede. Figure 1. Phase-angle polarization dependence for Europa, observations in the R filter (open circles) and the best fit result for the RT-CB modeling (solid line). References Rosenbush, V., Kiselev, N., Afanasiev, V. Icy moons of the outer planets. In: Polarimetry of Stars and Planetary Systems. (Eds. L. Kolokolova, J. Hough, A-Ch. Levasseur-Regourd), Cambridge University Press, Cambridge, 340-359. 2015. Muinonen, K., Penttilä, A., and Videen. Multiple scattering of light in particulate planetary media. In: Polarimetry of Stars and Planetary Systems. (Eds. L. Kolokolova, J. Hough, A-Ch. Levasseur-Regourd), Cambridge University Press, Cambridge, 117-129. 2015.

The aim of this project is to derive reference phase functions and their parameters using data from the ATLAS survey. The reference phase function corrects for the observation geometry by removing the influence of the asteroid shape by normalizing it to a sphere. (Muinonen et al. 2020)The ATLAS survey performed photometric observations in two filters: cyan (420-650 nm) and orange (560 - 820 nm) for over 180 000 asteroids at phase angles even below 1 deg (Heinze et al. 2018). Mahlke et al. (2021) derived over 1270 000 phase curve parameters using the ATLAS photometry, but they were corresponding to different viewing geometries, so they cannot be directly compared with each other.Traditional phase curves are derived based on lightcurve brightness maximum (or mean) values at a given phase angle. When using sparse photometry (e.g., Gaia, ATLAS), the observational geometry can substantially change between observations and objects. As a result, it is challenging to compare phase curves obtained for different asteroids (even if they were observed at the same epoch). If enough photometry is available, one can account for brightness changes due to shape, rotation, and aspect changes by moving to a reference phase function, which can be directly compared with the phase functions of other objects. (Muinonen et al. 2020, Martikainen et al. 2021, Wilawer et al. 2022)We derive the reference phase functions for ~2750 asteroids with models derived by Ďurech et al. (2020) using ATLAS photometric data. As a result, for each object, we will derive two reference phase functions: one for each ATLAS filter.This work has been supported by grant No. 2017/25/B/ST9/00740 from the National Science Centre, Poland.ReferencesĎurech, J., J. Tonry, N. Erasmus, L. Denneau, A. N. Heinze, H. Flewelling, and R. Vanco. ‘Asteroid Models Reconstructed from ATLAS Photometry’. Astronomy & Astrophysics 643 (November 2020): A59. https://doi.org/10.1051/0004-6361/202037729.Heinze, A. N., J. L. Tonry, L. Denneau, H. Flewelling, B. Stalder, A. Rest, K. W. Smith, S. J. Smartt, and H. Weiland. ‘A First Catalog of Variable Stars Measured by the Asteroid Terrestrial-Impact Last Alert System (ATLAS)’. The Astronomical Journal 156, no. 5 (November 2018): 241. https://doi.org/10.3847/1538-3881/aae47f.Mahlke, Max, Benoit Carry, and Larry Denneau. ‘Asteroid Phase Curves from ATLAS Dual-Band Photometry’. Icarus 354 (January 2021): 114094. https://doi.org/10.1016/j.icarus.2020.114094.Martikainen, J., K. Muinonen, A. Penttilä, A. Cellino, and X.-B. Wang. ‘Asteroid Absolute Magnitudes and Phase Curve Parameters from Gaia Photometry’. Astronomy & Astrophysics 649 (May 2021): A98. https://doi.org/10.1051/0004-6361/202039796.Muinonen, K., J. Torppa, X.-B. Wang, A. Cellino, and A. Penttilä. ‘Asteroid Lightcurve Inversion with Bayesian Inference’. Astronomy & Astrophysics 642 (October 2020): A138. https://doi.org/10.1051/0004-6361/202038036.Wilawer, E, D Oszkiewicz, A Kryszczyńska, A Marciniak, V Shevchenko, I Belskaya, T Kwiatkowski, et al. ‘Asteroid Phase Curves Using Sparse Gaia DR2 Data and Differential Dense Light Curves’. Monthly Notices of the Royal Astronomical Society 513, no. 3 (May 2022): 3242–51. https://doi.org/10.1093/mnras/stac1008.

Background: Spectral observations in visual and near-infrared wavelengths are used to infer their surface material composition. Similar laboratory measurements of meteorites and various minerals and are used to link the known composition in laboratory measurements to asteroid composition. However, many parameters in observations and measurements can introduce effects on the resulting spectra. With regolith-type powdered grains packed to a slab, the observing angles, particle size distribution, particle shapes, and space-weathering state of the material can all alter the spectra. Here, we try to model the particle size effects so that at least this effect could be understood when comparing different spectra. Size effects in spectra: One can find spectral measurements of the same material but with varying size fractions in spectral databases such as RELAB (https://pds-speclib.rsl.wustl.edu/) and SSHADE (https://www.sshade.eu/). The typical spectral effects of different particle size are that the smaller particles are generally brighter, have redder slope, and deeper (absolute) absorption band depths. However, it is also possible to find counterexamples of different behavior. Trend from light-scattering theory: If we limit to optically large particles (several times larger than the wavelength) and assume that different particle sizes are simply scaled versions of one particle, the particle size effects in spectra can be understood as interplay between surface reflections and absorption in the volume. If we assume that the surfaces are flat in the wavelength-scale, the surface reflections follow Fresnel reflections. For light that is refracted from the surface into the homogeneous material, the Beer-Lambert absorption gives the attenuation in the volume. The Fresnel-type reflections do not absorb and are also only weakly dependent on the imaginary part k of the complex refractive index of the material, m=n+ik. The Beer-Lambert absorption, on the other hand, is only dependent on k and the distance traveled in the material, d. If the same volume is divided into smaller particles, typical d in the material between air-surface or surface-air interfaces and reflections or refractions from these is decreasing. Since absorption is taking place only in the volume, the increased surface reflections are increasing the brightness. This is the simple mechanism behind increasing brightness with decreasing particle size. At the same time, the exponent-term in the Beer-Lambert absorption affects so that similar change in d in the particle for a bright material has larger effect than the same d in darker material. This means that the absorption band depths are also increasing, in absolute units, when particle size is decreasing. The possible increase of red slope with decreasing particle size in spectra cannot be explained with optically large particles. The longer wavelengths are ‘seeing’ the distances inside the particles shorter, but the effect is quite small for particles that are several times larger than the wavelength. However, if the sample also includes wavelength-scale particles, these are relatively more abundant in smaller size fractions and can introduce a red slope. This is because the scattering efficiency of particles increase when they reach wavelength-scale whereas for optically large particles it is constant. Numerical modeling: We will verify and quantify the abovementioned theoretical trends with numerical simulations. We use a two-fold scheme where we first simulate the single-scattering properties (single-scattering albedo and the phase function) of individual random particle shapes, and then simulate the multiple-scattering effect in a packed slab of these particles. We model the particles with a Voronoi cell particle model, see Fig. 1. In this model, a large volume is first filled with random seed points. Then, a 3d Voronoi division is done on the points, resulting the volume to be divided into Voronoi cells having flat surfaces and sharp corners. Finally, single cells are extracted from the volume, except the cells close to the edge of the volume to avoid edge-effects. The light-scattering properties of single Voronoi particles are computed using a geometric-optics ray-tracing code SIRIS (https://bitbucket.org/planetarysystemresearch/siris4-framework/). These computations are run for 200 realizations of the particle model and changing the size parameter (physical size divided by the wavelength) and the real and imaginary parts of the refractive index. The results are averaged over the particle shape realizations. The single-particle properties are fed into the Monte Carlo radiative transfer code RT-CB (https://bitbucket.org/planetarysystemresearch/rtcb_public/) where the amount of reflected light from a large slab containing the single particles is computed. This gives us the brightness as a function of particle size, wavelength, and real and imaginary parts of the refractive index. Preliminary results: We have a grid of size parameters and refractive indices computed, and the results are consistent with what we expected from the simple theory of the changing ratio of surface reflections to volume absorption. We can, for example, plug in a typical behavior of the imaginary part of olivine as a function of wavelength, keep the real part of the refractive index constant for simplicity (it does not change much in visual/near-infrared wavelengths), and plot the spectra of different-sized olivine particles, see Fig. 2. Conclusions and future work: Currently, we are increasing the parameter grid to include both smaller size parameters and smaller imaginary k values. From the results we have, it seems that we can fit an analytical function to the results with quite small prediction errors. If successful, this analytical model can be used to model the size effect on the reflectance spectra of particulate materials if the particles are clearly larger than the wavelength. If we can model, we can also remove the effect if we know the particle sizes and receive size-standardized spectra that can be better compared between the samples. As a side product, we can use this data and the model to invert the imaginary part of the refractive index for materials from which we have reflectance spectra measurements and the particle size.

The km-scale near-Earth object (1566) Icarus has an extremely eccentric orbit with a perihelion of q = 0.187 au and is classified as a potentially hazardous asteroid (PHA). It has been suspected to be the larger component of an asteroid pair, with the smaller object 2007 MK6, that is dynamically adjacent to the Taurid-Perseid meteor shower (Ohsutka et al., 2007; Kasuga & Jewitt, 2019). The low radar albedo of ~2% and photometric behavior at high phase angles together suggest a high-porosity surface with a high macroscopic roughness (Greenberg, et al. 2017; Ishiguro, et al., 2017). Delay-Doppler and visible lightcurve observations indicate a retrograde spin with a rapid rotation period of ~2.26 hr (Greenberg, et al. 2017; Warner et al., 2009).Combining visible spectrophotometry from the 24-Color Asteroid Survey (Chapman et al., 2020) and MITHNEOS near-infrared reflectance spectra (Binzel et al., 2019), we classify Icarus (Figure 1) as a slightly space weathered LL chondrite via a band parameter analysis routine (MacLennan, et al. in prep.). Using archived lightcurve observations of Icarus collected in 1968 and 2015 (Lagerkvist et al., 1993; Warner et al., 2009), and informed by spin axis constraints, we implement a Bayesian lightcurve inversion approach (Muinonen, et al. 2020) to construct a convex shape model of Icarus (Figure 2).Figure 1. Combined visible spectrophotometry and near-infrared reflectance spectra of Icarus and reflectance spectrum of the LL4 ordinary chondrite Hamlet from the RELAB database.Figure 2. Convex shape model of Icarus from inversion of lightcurve photometry.We incorporate thermal infrared data from the Spitzer Space Telescope (IRAC photometry and IRS spectra) and the NEOWISE survey in order to characterize Icarus’s thermophysical properties. We estimate the effective diameter and thermal inertia to be 1.4 ± 0.2 km and 60 ± 40 J K-1 m-2 s-1/2, respectively, with moderate surface roughness. The relatively low thermal inertia is consistent with a high porosity surface and/or a fine-grained lunar like surface. The latter interpretation is in contradiction to the polarization-phase relationship that suggests larger regolith grains (Ishiguro et al., 2007). We attempt to reconcile these different measurement results in our presentation.The physical characteristics of this extreme object are important for informing various resurfacing processes that have been proposed to be relevant for rapidly rotating objects, near-Sun asteroids, and spectrally-fresh Q-type asteroids (Graves et al., 2018, 2019). We thus consider our results in the context of these resurfacing processes.References:Binzel, R.P., et al. (2019) “Compositional distributions and evolutionary processes for the near-Earth object population: Results from the MIT-Hawaii Near-Earth Object Spectroscopic Survey (MITHNEOS)” Icarus, 324, 41–76.Chapman, C.R., Gaffey, M., and McFadden, L. (2020) 24-color Asteroid Survey V1.0. urn:nasa:pds:gbo.ast.24-color-survey::1.0. NASA Planetary Data System.Greenberg, A., et al. (2017) “Asteroid 1566 Icarus’s Size, Shape, Orbit, and Yarkovsky Drift from Radar Observations” AJ, 153:108.Graves, et al. (2018) “Resurfacing asteroids from YORP spin-up and failure”, Icarus, 304 (2018) 162–171.Graves, et al. (2019) “Resurfacing asteroids from thermally induced surface degradation”, Icarus, 322 (2019) 1–12.Ishiguro, M., et al. (2017) “Polarimetric Study of Near-Earth Asteroid (1566) Icarus”, AJ, 154:180.Kasuga, T. & Jewitt, D. (2019) “Asteroid-Meteorite Complexes”, In Meteoroids: Sources of Meteors on Earth and Beyond (Ed. G. Ryabova, D. Asher, & M. Campbell-Brown).Lagerkvist, C.-I. and Magnusson, P., Eds., (2011) Asteroid Photometric Catalog V1.1. EAR-A-3-DDR-APC-LIGHTCURVE-V1.1. NASA Planetary Data System.MacLennan, E.M., et al. (in prep) “Empirical characterization of space weathering on ordinary chondrite-like asteroids”.Muinonen , J. Torppa , X.-B. Wang , A. Cellino , and A. Penttilä (2020) “Asteroid lightcurve inversion with Bayesian inference”, A&A, 642, A138.Ohtsuka, K. “Apollo asteroids 1566 Icarus and 2007 MK6: Icarus Family Members?” AJ, 668: L71–L74.Warner, B.D., Harris, A.W., Pravec, P. (2009). “The Asteroid Lightcurve Database”, Icarus 202, 134-146.

Aims. We produce a clean and well-characterised catalogue of objects within 100 pc of the Sun from the Gaia Early Data Release 3. We characterise the catalogue through comparisons to the full data release, external catalogues, and simulations. We carry out a first analysis of the science that is possible with this sample to demonstrate its potential and best practices for its use., Methods. Theselection of objects within 100 pc from the full catalogue used selected training sets, machine-learning procedures, astrometric quantities, and solution quality indicators to determine a probability that the astrometric solution is reliable. The training set construction exploited the astrometric data, quality flags, and external photometry. For all candidates we calculated distance posterior probability densities using Bayesian procedures and mock catalogues to define priors. Any object with reliable astrometry and a non-zero probability of being within 100 pc is included in the catalogue., Results. We have produced a catalogue of 331 312 objects that we estimate contains at least 92% of stars of stellar type M9 within 100 pc of the Sun. We estimate that 9% of the stars in this catalogue probably lie outside 100 pc, but when the distance probability function is used, a correct treatment of this contamination is possible. We produced luminosity functions with a high signal-to-noise ratio for the main-sequence stars, giants, and white dwarfs. We examined in detail the Hyades cluster, the white dwarf population, and wide-binary systems and produced candidate lists for all three samples. We detected local manifestations of several streams, superclusters, and halo objects, in which we identified 12 members of Gaia Enceladus. We present the first direct parallaxes of five objects in multiple systems within 10 pc of the Sun., Conclusions. We provide the community with a large, well-characterised catalogue of objects in the solar neighbourhood. This is a primary benchmark for measuring and understanding fundamental parameters and descriptive functions in astronomy.

The Legacy Survey of Space and Time (LSST) is one of the ongoing or future surveys, together with the Gaia and Euclid missions, which will produce a wealth of spectrophotometric observations of asteroids. This article shows how deep learning techniques with neural networks can be used to classify the upcoming observations, particularly from LSST, into the Bus-DeMeo taxonomic system. We report here a success ratio in classification up to 90.1% with a reduced set of Bus-DeMeo types for simulated observations using the LSST photometric filters. The scope of this work is to introduce tools to link future observations into existing Bus-DeMeo taxonomy.

The spectral bidirectional reflectance distribution function (BRDF) maps incident radiation of a surface to its outgoing counterpart at different wavelengths. This function plays a fundamental role in characterizing the various types of earth surfaces. Due to its high dimensionality, the measurements, analysis, and simulation of spectral BRDF are challenging. In this letter, we introduce a new method for processing spectral reflectance using the so-called data-adjacency, i.e., the correlation between adjacent wavelengths and viewing directions. The results show that the benefits of efficient representation, noise reduction, and analysis capability can all be integrated to the data. © 2019 IEEE. This work was supported by the Academy of Finland Consortium Project Albedo under Project 298137 and Project 298139.

The Gaia mission of the European Space Agency (ESA) was launched in December 2013 and began it scientific operations in July 2014. Gaia is essentially devoted to the measurement of positions, parallaxes, proper motions, brightnesses, and colours of stars. However, Gaia has also obtained astrometric, photometric, and spectroscopic measurements for several hundreds of thousands of asteroids. The Gaia Data Release 3 (DR3) is the first to contain low resolution reflectance spectra of 60,518 solar system small bodies, the large majority of which are asteroids of the main belt (Gaia collaboration, Galluccio, Delbo et al. 2022). The global survey properties, the methods of data production and validation are detailed in the aforementioned paper published by the journal Astronomy and Astrophysics, which accompanies the DR3, and also summarised in the presentation of Galluccio et al. (2022) at this conference (EPSC 2022). Here we present preliminary results about the Gaia view of asteroid collisional families. We identified asteroids belonging to families during the validation of Gaia asteroid spectra. Based on the family identification of Nesvorny et al. (2015), with the addition of the New Polana and the Eulalia families from Walsh et al. (2013), we found that in the Gaia DR3 there are 25,088 asteroids that belong to 116 collisional asteroid families of the 121 listed in Tab.1. This table also reports the number of family members and the number of members with a Gaia DR3 reflectance spectrum. However, the family identification of current catalogues is conservative by construction in order to keep good separation between the families. Hence, it is very likely that (i) some of the known families are more extended than what is available in current catalogues, namely, that catalogues based on dynamical criteria do not capture the whole extent of a family, and (ii) some unknown families are yet to be identified. This implies that the aforementioned number of asteroid family members with Gaia DR3 reflectance spectra is likely an estimation lower than the true number. We will present some important features that Gaia observed in families. One of these is the correlation between some spectral parameters, such as the slope and the depth of the 1-micron absorption band of the reflectance spectrum, and the age of members of asteroid families belonging to the so called spectroscopic S-complex (DeMeo et al. 2009). These correlations can be explained in terms of a space weathering process that reddens and reduces the 1-band depth as a function of time on S-complex asteroids. For the brightest asteroids, the extension of Gaia reflectance spectra at wavelengths shorter than 0.45 micron is very useful for distinguishing the composition of primitive, carbonaceous asteroid families, which are difficult to be discriminated with the ground based spectroscopic data currently present in the literature. References: - DeMeo, F. E., Binzel, R. P., Slivan, S.~M., Bus, S. J. 2009. Icarus 202, 160–180. - Gaia collaboration, Galluccio, Delbo et al. 2022. A&A under review. - Nesvorný, D., Brož, M., & Carruba, V. 2015. in Asteroids IV (P. Michel, et al. eds.) University of Arizona Press, Tucson., - Walsh, K. J., Delbo, M., et al. 2013. Icarus 225, 283–297.

The ESA-JAXA BepiColombo mission will provide simultaneous measurements from two spacecraft, offering an unprecedented opportunity to investigate magnetospheric and exospheric dynamics at Mercury as well as their interactions with the solar wind, radiation, and interplanetary dust. Many scientific instruments onboard the two spacecraft will be completely, or partially devoted to study the near-space environment of Mercury as well as the complex processes that govern it. Many issues remain unsolved even after the MESSENGER mission that ended in 2015. The specific orbits of the two spacecraft, MPO and Mio, and the comprehensive scientific payload allow a wider range of scientific questions to be addressed than those that could be achieved by the individual instruments acting alone, or by previous missions. These joint observations are of key importance because many phenomena in Mercury's environment are highly temporally and spatially variable. Examples of possible coordinated observations are described in this article, analysing the required geometrical conditions, pointing, resolutions and operation timing of different BepiColombo instruments sensors., Comment: 78 pages, 14 figures, published

The Gaia mission of the European Space Agency (ESA) published its third release (DR3) on June 13, 2022, including for the first time a survey of 60 518 mean reflectance spectra of Solar System objects (SSOs). Each reflectance spectrum was derived from calibrated measurements obtained by the onboard Blue and Red low-resolution spectro-photometers (BP/RP) and consists of sixteen discrete wavelength bands, along with additional information about the data quality for each band. We will describe the processing of the Gaia spectral data of SSOs and the steps of our internal validation procedures. We present the adopted approach for external validation against SSO reflectance spectra available in the literature, obtained from ground-based and space-borne telescopes, to assess the quality of Gaia SSO reflectance spectra. This work summarizes a more detailed description by Galluccio et al. (2022) [1]. Introduction Gaia DR3 contains information for a sample of more than 150,000 SSOs, including astrometry, photometry, osculating elements, and mean reflectance spectra [2]. The selection of these objects is described by Tanga et al. (2022) [2]. Based on the quality of the data and some criteria developed hereafter, DR3 contains 60518 mean reflectance spectra of Near-Earth Asteroids (NEAs), main-belt asteroids, Jupiter Trojans, transneptunian objects (TNOs), and other classes (Table 1) observed at relatively large phase angles (~20°). Table 1: No. of SSOs with Gaia DR3 spectra for each of the dynamical classes listed on the NASA JPL website. The classes are defined according to the criteria based on the orbital semi-major axis a, the perihelion distance q, and the aphelion distance Q. Dynamical Class No. of SSO Criterion (values in au) NEA Aten 6 a < 1.0 & Q > 0.983 NEA Apollo 52 a > 1.0 & q < 1.017 NEA Amor 47 1.017 < q < 1.3 Mars-Crosser 729 1.3 < q < 1.666 Inner Main Belt 1 221 a < 2.0 & q > 1.666 Main Belt 55 976 2.0 < a < 3.2 & q > 1.666 Outer Main Belt 1 995 3.2 < a < 4.6 Jupiter Trojan 477 4.6 < a < 5.5 Centaur 5 4.6 < a < 5.5 TNO 7 a > 30.1 Other 2 none of the above Production of SSO reflectance spectra The first step in computing the SSO mean reflectance spectra consisted of a calibration of the BP/RP spectra and removal of all instrumental and astrophysical effects to produce internally calibrated epoch spectra [3]. Each of them is an array of 60 internal flux measurements and corresponding uncertainties, computed for each one of the 60 pixel-long XP (BP/RP). The BP operates in the wavelength range λ between 330 and 680 nm, and RP between 640 and 1050 nm. Next, BP and RP epoch reflectance R(λi)t were determined by dividing the flux ft(λi) of each SSO spectrum at the epoch t by the reference solar analogue spectrum F(λ). The latter has been computed by averaging Gaia DR3 mean spectra of several known solar analogue stars widely used in asteroid ground-based spectroscopy because their spectra closely mimic the one of our Sun. Epoch reflectance was then normalized at λ = 550 nm. To compute the mean reflectance spectrum, we first defined a set of fixed wavelength bands, each one having a width of 44 nm, in the interval from 374 nm to 1034 nm. Inside each wavelength band, we computed a weighted average reflectance using all epoch reflectance present in each bin after applying a sigma-clipping procedure (see Figure 1). Figure 1: Example of the mean computed reflectance R(λi) (black circles) for the asteroid (61) Danae. The grey points are the R(λi)t corresponding to each epoch reflectance. The R(λi) t values accepted by our filtering method are coloured in blue (BP) and red (RP). Some filters based on SNR and on quality criteria were finally applied to the sample of computed mean reflectance spectra. Along with the mean reflectance spectra, the Gaia DR3 catalogue also contains for each source a reflectance_spectrum_flag field, indicating the overall quality of the resulting reflectance spectrum. Validation The validation of the Gaia DR3 mean reflectance spectra was obtained by studying and comparing spectral parameters including the spectral slope and the absorption band depth around 900 nm (equivalent to SDSS z-i colour) with those available in the literature, including the SMASSII survey [4] (Figure 2), ground-based observations at large phase angle [5] or space-borne telescope spectra. In general, Gaia DR3 mean reflectance spectra are in good agreement with the literature data. No significant spectral reddening was detected during the validation step. Figure 2: z colour vs. spectral slope of the asteroids of DR3 (grey dots). Over-plotted with circles of different colours are the same spectral parameters computed by us (see Section 4.2) for the asteroids of SMASSII [4]. The letters C, S, and X represent taxonomic complexes, the other letters spectral classes Conclusions Gaia DR3 includes the largest space-based survey of reflectance spectra of Solar System small bodies observed at visible wavelengths with excellent quality. In the presentation of Delbo et al. (2022) at this conference some preliminary results about the Gaia view of asteroid collisional families will be described. Acknowledgements This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. References [1] Gaia collaboration, Galluccio, Delbo et al. 2022 Gaia Data Release 3: Reflectance spectra of Solar System Small Bodies. A&A under review. [2] Gaia collaboration, Tanga et al. 2022 Gaia Data Release 3: the Solar System survey. A&A under review. [3] De Angeli et al. 2022, Gaia Data Release 3: Processing and validation of BP/RP low-resolution spectral data A&A under review.[4] Bus and Binzel. 2002. Icarus 158, 146-177.[5] Cellino, Bendjoya, Delbo’ et al. 2020. A&A, 642, A80

We present a multi-scale light-scattering model that is capable of simulating the reflectance spectra of a regolith layer. In particular, the model can be applied to a case where the regolith grains have varying amounts of nanophase inclusions due to space weathering of the material. As different simulation tools are employed for different size scales of the target geometry (roughly, nano-, micro-, and millimeter scales), the particle size effects, the surface reflections, and the volume scattering can all be properly accounted for. Our results with olivine grains and nanophase iron inclusions verify the role of the nanoinclusions in the reflectance spectra of space-weathered materials. Together with the simulation results, we give simplified explanations for the space-weathering effects based on light scattering, namely the decrease of albedo, the general increase of the red spectral slope, and the dampening of the spectral bands. We also consider the so-called ultraviolet bluing effect and show how the change in the spectral slope over the ultraviolet-visual wavelengths is due to the decrease of reflectance in the visual wavelengths rather than the increase of reflectance in the ultraviolet part.

We explore the performance of neural networks in automatically classifying asteroids into their taxonomic spectral classes. We particularly focus on what the methodology could offer the ESA Gaia mission. We constructed an asteroid dataset that can be limited to simulating Gaia samples. The samples were fed into a custom-designed neural network that learns how to predict the samples’ spectral classes and produces the success rate of the predictions. The performance of the neural network is also evaluated using three real preliminary Gaia asteroid spectra. The overall results show that the neural network can identify taxonomic classes of asteroids in a robust manner. The success in classification is evaluated for spectra from the nominal 0.45–2.45 µm wavelength range used in the Bus-DeMeo taxonomy, and from a limited range of 0.45–1.05 µm following the joint wavelength range of Gaia observations and the Bus-DeMeo taxonomic system. The obtained results indicate that using neural networks to execute automated classification is an appealing solution for maintaining asteroid taxonomies, especially as the size of the available datasets grows larger with missions like Gaia.

We present first results from a polarimetric survey of asteroids in the near-infrared J and H bands (1.25 and 1.65 microns, respectively). This survey has been enabled by the newly commissioned WIRC-Pol instrument on the Palomar 5 m telescope. WIRC-Pol simultaneously senses the four linear polarization components from the target, while using a half-wave plate to beam swap between them. This setup allows us to obtain bandpass polarimetric accuracies better than 0.1% for our targets. WIRC-Pol also obtains low resolution spectra of each Stokes component, allowing us to investigate the spectropolarimetric properties of our targets as a function of phase. We show polarimetric phase curves for objects that have been sampled at multiple phases, our initial spectropolarimetric findings, and discuss the results from modeling these observations.

The Earth’s spherical albedo describes the ratio of light reflected from the Earth to that incident from the Sun, an important input variable for the Earth’s radiation balance. The spherical albedo has been previously estimated from satellites in low-Earth orbits, and from light reflected from the Moon. However, neither of these methods can produce continuous time series of the entire planet. We developed a global method to derive the Earth’s spherical albedo using the images from the Earth Polychromatic Imaging Camera (EPIC) on board NOAA’s Deep Space Climate Observatory (DSCOVR). The satellite is located in the Lagrange 1 point between the Earth and the Sun and observes the complete illuminated part of the Earth at once. The method allows us to provide continuously updated spherical albedo time series data starting from 2015. This time series shows a systematic seasonal variation with the mean annual albedo estimated as 0.295±0.008 and an exceptional albedo maximum in 2020, attributed to unusually abundant cloudiness over the Southern Oceans.

Atmospheric ice crystals scatter sunlight, affecting Earth’s climate through the radiation properties of cirrus clouds. Naturally occuring surface roughness and its effect on the scattering properties of ice crystals remain largely unknown. Scattering by ice crystals with rough surfaces is studied by placing a finite, thin surface-roughness element on an infinitely large, planar vacuum-ice boundary. The elements are generated using a statistical model based on fractional Brownian motion. The horizontal roughness scale is described by the Hurst exponent H and the vertical roughness scale with the root-mean-square roughness parameter R q . The computations are performed with the surface mode of the Discrete Dipole Approximation software ADDA (version 1.34b). Several incident directions for wavelength of 0.5 μ m from both above and below the planar surface are studied. A refractive index for ice m = 1.313 + i 5.889 · 10 − 10 is used throughout the computations. Results are averaged over ten rough surface realizations for a specific H , R q -pair. Scattering by the rough elements is compared to that by the corresponding smooth elements. The rougher the element is, the more of the scattered intensity is transmitted through the surface. The rough elements have distinctively smoother angular distributions for the degree of linear polarization than their smooth counterparts. Also, it is found that while roughness itself affects polarization, the exact surface morphology does not seem to have a significant effect. The vertical roughness scale R q has a larger effect on the light scattering results than the horizontal scale H . Enhanced angular scattering is detected in directions nearly parallel to the vacuum-ice boundary within the ice medium. The phenomenon is explained with a strong internal reflection mechanism. The model for surface roughness, along with the light scattering methodology used here, could be incorporated into geometric optics ray-tracing computations for large ice crystals and other particles.

The shapes and rotational states of main-belt asteroids are important for understanding their formation and evolution. Available photometric data of asteroids are biased due to selection effects, including the relative paucity of analyses of slowly rotating objects. In order to get photometric data of slowly rotating asteroids, an international joint observation project has been carried out since 2015 using Chinese and SARA (Southeastern Association for Research in Astronomy) telescopes. In this paper, the photometric data of one of this project targets – (103) Hera were analyzed using the convex inversion method and Lommel-Seeliger ellipsoid model. Combining existing and new photometric data, we re-calculated the shape and spin parameters for (103) Hera. Using a convex shape method, a pair of poles are derived for (103) Hera – ( 83 . 0 ∘ , 39 . 0 ∘ ) and ( 269 . 7 ∘ , 56 . 8 ∘ ) in ecliptic frame. The spin periods corresponding to these poles are very close – 23.74264 h and 23.74267 h respectively. Meanwhile, the same data were analyzed using the Lommel-Seeliger ellipsoid inversion method and a pair of pole solutions – ( 74 . 1 ∘ , 39 . 0 ∘ ) and ( 263 . 1 ∘ , 51 . 0 ∘ ) with a spin period of 23.74262 h and 23.74263 h respectively are derived. Based on the derived shape of (103) Hera, we have fitted the H, G 1 , G 2 phase function using the calibrated data after removing effects of aspheric shape. As a result, we estimated its absolute magnitude H = 8.92 mag with two phase function parameters G 1 = 0.13 and G 2 = 0.45.

Aims. We perform light curve inversion for 491 asteroids to retrieve phase curve parameters, rotation periods, pole longitudes and latitudes, and convex and triaxial ellipsoid shapes by using the sparse photometric observations from Gaia Data Release 2 and the dense ground-based observations from the DAMIT database. We develop a method for the derivation of reference absolute magnitudes and phase curves from the Gaia data, allowing for comparative studies involving hundreds of asteroids. Methods. For both general convex shapes and ellipsoid shapes, we computed least-squares solutions using either the Levenberg-Marquardt optimization algorithm or the Nelder-Mead downhill simplex method. Virtual observations were generated by adding Gaussian random errors to the observations, and, later on, a Markov chain Monte Carlo method was applied to sample the spin, shape, and scattering parameters. Absolute magnitude and phase curve retrieval was developed for the reference geometry of equatorial illumination and observations based on model magnitudes averaged over rotational phase. Results. The derived photometric slope values showed wide variations within each assumed Tholen class. The computed Gaia G-band absolute magnitudes matched notably well with the V-band absolute magnitudes retrieved from the Jet Propulsion Laboratory Small-Body Database. Finally, the reference phase curves were well fitted with the H, G1, G2 phase function. The resulting G1, G2 distribution differed, in an intriguing way, from the G1, G2 distribution that is based on the phase curves corresponding to light curve brightness maxima.

Aims. We explore the performance of neural networks in automatically classifying asteroids into their taxonomic spectral classes. We particularly focus on what the methodology could offer the ESA Gaia mission. Methods. We constructed an asteroid dataset that can be limited to simulating Gaia samples. The samples were fed into a custom-designed neural network that learns how to predict the samples’ spectral classes and produces the success rate of the predictions. The performance of the neural network is also evaluated using three real preliminary Gaia asteroid spectra. Results. The overall results show that the neural network can identify taxonomic classes of asteroids in a robust manner. The success in classification is evaluated for spectra from the nominal 0.45–2.45 μm wavelength range used in the Bus-DeMeo taxonomy, and from a limited range of 0.45–1.05 μm following the joint wavelength range of Gaia observations and the Bus-DeMeo taxonomic system. Conclusions. The obtained results indicate that using neural networks to execute automated classification is an appealing solution for maintaining asteroid taxonomies, especially as the size of the available datasets grows larger with missions like Gaia.

Since July 2014, the ESA Gaia mission has been surveying the entire sky down to magnitude 20.7 in the visible. In addition to the millions of stars, thousands of Solar System Objects (SSOs) are observed daily. By comparing their positions to those of known objects, a daily processing pipeline filters known objects from potential discoveries. However, owing to Gaia's specific scanning law designed for stars, potential newly discovered moving objects are characterized by very few observations, acquired over a limited time. This aspect was recognized early in the design of the Gaia data processing. A daily processing pipeline dedicated to these candidate discoveries was set up to release calls for observations to a network of ground-based telescopes. Their aim is to acquire follow-up astrometry and to characterize these objects. From the astrometry measured by Gaia, preliminary orbital solutions are determined, allowing to predict the position of these potentially new discovered objects in the sky accounting for the large parallax between Gaia and the Earth (separated by 0.01 au). A specific task within the Gaia Consortium has been responsible for the distribution of requests for follow-up observations of potential Gaia SSO discoveries. Since late 2016, these calls for observations (called alerts) are published daily via a Web interface, freely available to anyone world-wide. Between November 2016 and July 2020, over 1700 alerts have been published, leading to the successful recovery of more than 200 objects. Among those, six have provisional designation assigned with the Gaia observations, the others being previously known objects with poorly characterized orbits, precluding identification at the time of Gaia observations. There is a clear trend for objects with a high inclination to be unidentified, revealing a clear bias in the current census of SSOs against high inclination populations., Submitted to Astronomy & Astrophysics

We study the scattering properties of a cloud of particles. The particles are spherical, close to the incident wavelength in size, have a high albedo, and are randomly packed to 20% volume density. We show, using both numerically exact methods for solving the Maxwell equations and radiative-transfer-approximation methods, that the scattering properties of the cloud converge after about ten million particles in the system. After that, the backward-scattered properties of the system should estimate the properties of a macroscopic, practically infinite system. (C) 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Aims. We aim to demonstrate the scientific potential of the Gaia Early Data Release 3 (EDR3) for the study of different aspects of the Milky Way structure and evolution and we provide, at the same time, a description of several practical aspects of the data and examples of their usage., Methods. We used astrometric positions, proper motions, parallaxes, and photometry from EDR3 to select different populations and components and to calculate the distances and velocities in the direction of the anticentre. In this direction, the Gaia astrometric data alone enable the calculation of the vertical and azimuthal velocities; also, the extinction is relatively low compared to other directions in the Galactic plane. We then explore the disturbances of the current disc, the spatial and kinematical distributions of early accreted versus in situ stars, the structures in the outer parts of the disc, and the orbits of open clusters Berkeley 29 and Saurer 1., Results. With the improved astrometry and photometry of EDR3, we find that: (i) the dynamics of the Galactic disc are very complex with oscillations in the median rotation and vertical velocities as a function of radius, vertical asymmetries, and new correlations, including a bimodality with disc stars with large angular momentum moving vertically upwards from below the plane, and disc stars with slightly lower angular momentum moving preferentially downwards; (ii) we resolve the kinematic substructure (diagonal ridges) in the outer parts of the disc for the first time; (iii) the red sequence that has been associated with the proto-Galactic disc that was present at the time of the merger with Gaia-Enceladus-Sausage is currently radially concentrated up to around 14 kpc, while the blue sequence that has been associated with debris of the satellite extends beyond that; (iv) there are density structures in the outer disc, both above and below the plane, most probably related to Monoceros, the Anticentre Stream, and TriAnd, for which the Gaia data allow an exhaustive selection of candidate member stars and dynamical study; and (v) the open clusters Berkeley 29 and Saurer 1, despite being located at large distances from the Galactic centre, are on nearly circular disc-like orbits., Conclusions. Even with our simple preliminary exploration of the Gaia EDR3, we demonstrate how, once again, these data from the European Space Agency are crucial for our understanding of the different pieces of our Galaxy and their connection to its global structure and history.

The Apollo-type near-Earth asteroid (155140) 2005 UD is thought to be a member of the Phaethon-Geminid meteor stream Complex (PGC). Its basic physical parameters are important for unveiling its origin and its relationship to the other PGC members as well as to the Geminid stream. Adopting the Lommel-Seeliger ellipsoid method and $H,G_1,G_2$ phase function, we carry out spin, shape, and phase curve inversion using the photometric data of 2005~UD. The data consists of 11 new lightcurves, 3 lightcurves downloaded from the Minor Planet Center, and 166 sparse data points downloaded from the Zwicky Transient Facility database. As a result, we derive the pole solution of ($285^\circ.8^{+1.1}_{-5.3}$, $ -25^\circ.8^{+5.3}_{-12.5}$) in the ecliptic frame of J2000.0 with the rotational period of $5.2340$ h. The corresponding triaxial shape (semiaxes $a>b>c$) is estimated as $b/a= 0.76^{+0.01}_{-0.01}$ and $c/a=0.40^{+0.03}_{-0.01}$. Using the calibrated photometric data of 2005 UD, the $H,G_1,G_2$ parameters are estimated as $17.19^{+0.10}_{-0.09}$ mag, $0.573^{+0.088}_{-0.069}$, and $0.004^{+0.020}_{-0.021}$, respectively. Correspondingly, the phase integral $q$, photometric phase coefficient $k$, and the enhancement factor $��$ are 0.2447, -1.9011, and 0.7344. From the values of $G_1$ and $G_2$, 2005 UD is likely to be a C-type asteroid. We estimate the equivalent diameter of 2005 UD from the new $H$-value: it is 1.30 km using the new geometric albedo of 0.14., Has submitted to Planetary and Space Science

We present the early installment of the third Gaia data release, Gaia EDR3, consisting of astrometry and photometry for 1.8 billion sources brighter than magnitude 21, complemented with the list of radial velocities from Gaia DR2. Gaia EDR3 contains celestial positions and the apparent brightness in G for approximately 1.8 billion sources. For 1.5 billion of those sources, parallaxes, proper motions, and the (G_BP-G_RP) colour are also available. The passbands for G, G_BP, and G_RP are provided as part of the release. For ease of use, the 7 million radial velocities from Gaia DR2 are included in this release, after the removal of a small number of spurious values. New radial velocities will appear as part of Gaia DR3. Finally, Gaia EDR3 represents an updated materialisation of the celestial reference frame (CRF) in the optical, the Gaia-CRF3, which is based solely on extragalactic sources. The creation of the source list for Gaia EDR3 includes enhancements that make it more robust with respect to high proper motion stars, and the disturbing effects of spurious and partially resolved sources. The source list is largely the same as that for Gaia DR2, but it does feature new sources and there are some notable changes. The source list will not change for Gaia DR3. Gaia EDR3 represents a significant advance over Gaia DR2, with parallax precisions increased by 30 percent, proper motion precisions increased by a factor of 2, and the systematic errors in the astrometry suppressed by 30--40 percent for the parallaxes and by a factor ~2.5 for the proper motions. The photometry also features increased precision, but above all much better homogeneity across colour, magnitude, and celestial position. A single passband for G, G_BP, and G_RP is valid over the entire magnitude and colour range, with no systematics above the 1 percent level.

Full list of authors: Bunce, Emma J.; Martindale, Adrian; Lindsay, Simon; Muinonen, Karri; Rothery, David A.; Pearson, Jim; McDonnell, Ivor; Thomas, Chris; Thornhill, Julian; Tikkanen, Tuomo; Feldman, Charly; Huovelin, Juhani; Korpela, Seppo; Esko, Eero; Lehtolainen, Arto; Treis, Johannes; Majewski, Petra; Hilchenbach, Martin; Väisänen, Timo; Luttinen, Arto; Kohout, Tomas; Penttilä, Antti; Bridges, John; Joy, Katherine H.; Alcacera-Gil, Maria Angeles; Alibert, Guilhem; Anand, Mahesh; Bannister, Nigel; Barcelo-Garcia, Corinne; Bicknell, Chris; Blake, Oliver; Bland, Phil; Butcher, Gillian; Cheney, Andy; Christensen, Ulrich; Crawford, Tony; Crawford, Ian A.; Dennerl, Konrad; Dougherty, Michele; Drumm, Paul; Fairbend, Raymond; Genzer, Maria; Grande, Manuel; Hall, Graeme P.; Hodnett, Rosie; Houghton, Paul; Imber, Suzanne; Kallio, Esa; Lara, Maria Luisa; Balado Margeli, Ana; Mas-Hesse, Miguel J.; Maurice, Sylvestre; Milan, Steve; Millington-Hotze, Peter; Nenonen, Seppo; Nittler, Larry; Okada, Tatsuaki; Ormö, Jens; Perez-Mercader, Juan; Poyner, Richard; Robert, Eddy; Ross, Duncan; Pajas-Sanz, Miriam; Schyns, Emile; Seguy, Julien; Strüder, Lothar; Vaudon, Nathalie; Viceira-Martín, Jose; Williams, Hugo; Willingale, Dick; Yeoman, Tim.-- This is an open access article., The Mercury Imaging X-ray Spectrometer is a highly novel instrument that is designed to map Mercury’s elemental composition from orbit at two angular resolutions. By observing the fluorescence X-rays generated when solar-coronal X-rays and charged particles interact with the surface regolith, MIXS will be able to measure the atomic composition of the upper ∼10-20 μm of Mercury’s surface on the day-side. Through precipitating particles on the night-side, MIXS will also determine the dynamic interaction of the planet’s surface with the surrounding space environment. MIXS is composed of two complementary elements: MIXS-C is a collimated instrument which will achieve global coverage at a similar spatial resolution to that achieved (in the northern hemisphere only – i.e. ∼ 50 – 100 km) by MESSENGER; MIXS-T is the first ever X-ray telescope to be sent to another planet and will, during periods of high solar activity (or intense precipitation of charged particles), reveal the X-ray flux from Mercury at better than 10 km resolution. The design, performance, scientific goals and operations plans of the instrument are discussed, including the initial results from commissioning in space. © 2020, The Author(s)., The MIXS team has gratefully received funding from a consortium of agencies across Europe. The UK Space Agency are the lead funding agency, supported by national contributions from our amazing panEuropean team and the European Space Agency. UK funding has come from, the science and technology facilities council - STFC (grant numbers: PP/E002056/1; PP/E002412/1; ST/L000776/1; ST/M002101/1; ST/M002187/1; ST/N00339X/1; ST/N000471/1; ST/P001963/1; ST/S002596/1; ST/J000213/1), the United Kingdom Space Agency -UKSA (grant numbers: ST/P000908/1; ST/T001542/1; ST/K003194/1; ST/L000318/1; ST/M000702/1) and the European Space Agency -ESA (contract numbers: 4000118221/16/ES/JD; RES-PSS/NR/035-B/200; 20919/07/NF/FG). Images shown in Fig. 4, Fig. 6 and Fig. 9 are adapted from drawings produced by MagnaParva Ltd. under ESA contract number 20919/07/NL/FG. EJB is supported by a Royal Society Wolfson Research Merit Award. The DEPFET X-ray detectors were contributed with the support of dedicated Max Planck Society grants by MPG and MPS as well as ESA contract number 4000108312. The Spanish contribution was funded by MEC/MINECO/MICINN grants; AYA200803467/ESP, AYA2011-24780, AYA2012-39362-C02-01, ESP2014-59789-P and ESP2015-65712-C5-1-R. Finnish hardware contributions were funded by Tekes (now "Business Finland") during the era from 2004 to 2019. Research at the University of Helsinki is supported, in part, by the Academy of Finland (grant number 1325805).

Introduction At present, the main database of asteroid absolute magnitudes is the Minor Planet Center (MPC). The MPC receives asteroid magnitudes from many observatories in different spectral bands of different photometric systems, but calculates absolute magnitudes ​​for V band of the Johnson photometric system using the HG-function [1]. A comparison of the MPC absolute magnitudes (HMPC) with the dataset of high-quality absolute magnitudes obtained by Pravec et al. [2] revealed systematical differences between these datasets. The new HG1G2 function was recommended by Muinonen et al. [3] to be used for more precise calculating the asteroid absolute magnitudes. This function was calibrated according to good measured magnitude-phase dependences, and the average parameters ​​for major taxonomic classes of asteroids were obtained [4, 5]. Using these average values, it is possible to calculate the absolute magnitudes of asteroids from individual observations at different phase angles. For sparse photometric data, it was suggested to use the two-parameter HG12 system [3, 4, 6]. Recently, large-scale survey programs such as Pan-STARRS and Palomar Transient Factory (PTF) [7, 8] performed new observations, within which absolute magnitudes of asteroids have also been derived. Both datasets are homogeneous, but they were obtained mostly in the Sloan system and then transformed to the Johnson system. Comparison of these datasets of absolute magnitudes ​​with the MPC data showed systematical deviations [7, 8]. It should be noted that the absolute magnitudes of asteroids in the Pan-STARRS and PTF surveys [7, 8] were obtained in the new HG12 system. In addition, the work is continued to obtain the asteroid absolute magnitudes in the new system for PTF and Pan-STARRS datasets [9]. To check the reliability of these datasets and identify systematic deviations, an independent set of high-quality data on absolute magnitudes is required. Thus, we initiated an observational program to determine the absolute magnitudes of several hundred asteroids. Here we present preliminary results of our program. Results For our dataset, we used first the data of the asteroid magnitude-phase dependences collected at the Institute of Astronomy of V. N. Karazin Kharkiv National University [5, 10–12]. We also used observational data of asteroids from our other programs and performed new observations of some asteroids [13–14]. We calculated our absolute magnitude dataset in the Johnson V band with a correction for lightcurve variations using the HG1G2 system according to its extension to low-accuracy data [4]. In such manner, we obtained a homogenous dataset of absolute magnitudes of about 300 asteroids in the range from 6.5 to 16 mag. Fig. 1 shows the correlations of the absolute magnitudes from the MPC, Pan-STARRS (HPS), and PTF (HPTF) datasets with those of the Kharkiv dataset (HKH). Figure 1: Absolute magnitudes of MPC (HMPC), Pan-STARRS (HPS), and PTF (HPTF) vs. those of the Kharkiv dataset (HKH). We observe a high correlation between our dataset and the other three datasets. There are small differences in the constant terms and slopes that point out some systematical deviations especially for the MPC and the PTF datasets. Figure 2: Histogram of the absolute magnitude deviations between the Kharkiv and Pan-STARRS datasets. Figure 3: Histogram of the absolute magnitude deviations between the Kharkiv and MPC datasets. For the MPC dataset, we found a systematical deviation of about 0.1 mag (Fig. 3). It is less than that obtained in [2] and close to that obtained in [7]. The smallest deviations were found for the Pan-STARRS dataset. This is confirmed by the histogram of absolute magnitude deviations between the Kharkiv and Pan-STARRS datasets presented in Fig. 2. The solid line is a fit to the data using the Gaussian function. Conclusions We prepared a preliminary comparative analysis of the asteroid absolute magnitudes between the Kharkiv dataset and the MPC, Pan-STARRS, and PTF datasets. The analysis has shown that the absolute magnitude dataset obtained from the Pan-STARRS survey project is closest to our dataset and can be the most suitable for the determination of diameters or albedos of asteroids. Acknowledgments This research has made use of data and/or services provided by the International Astronomical Union's Minor Planet Center. References [1] Bowell, E., Hapke, B., Domingue, D., et al. In Asteroids II. Tucson. Univ. Arizona Press. P. 524−556, 1989. [2] Pravec, P., Harris, A.W., Kušnirák, P., et al. Icarus, 221, 365-387, 2012. [3] Muinonen, K., Belskaya, I.N., Cellino, A., et al. Icarus, 209, 542–555, 2010. [4] Penttilä, A. Shevchenko, V.G., Wilkman, O., Muinonen, K. PSS, 123, 117–125, 2016. [5] Shevchenko, V.G., Belskaya, I.N., Muinonen, K., et al. PSS, 123, 101−116, 2016. [6] Oszkiewicz, D.A., Muinonen, K., Bowell, E., et al. JQSRT, 112, 1919-1929, 2011. [7] Veres, P., Jedicke, R., Firzsimmons, A., et al. Icarus, 261, 34-47, 2015. [8] Waszczak, A., Chang, C.-K., Ofeck, E.O., et al. Astron. J., 150, A75, 2015. [9] Penttilä, A., Cellino A., Lu X., et al. DPS, 48, No 7, 228, 2016. [10] Shevchenko, V.G., Belskaya I.N., Lupishko D.F., et al. EAR-A-COMPIL-3-MAGPHASE-V1.0. NASA PDS, 2010. [11] Shevchenko, V.G., Belskaya, I.N., Slyusarev, I.G., et al. Icarus, 217, 202–208, 2012. [12] Slyusarev, I.G., Shevchenko, V.G., Belskaya, I.N., et al. LPSC 43, 1885, 2012. [13] Chiorny, V.G., Shevchenko V.G., Krugly Yu.N., et al. PSS, 55, 986−997, 2007. [14] Shevchenko, V.G., Mikhalchenko O.I., Belskaya I.N., et al. LPSC 50, Abstract #1771, 2019.

The optical constant of the material, meaning the complex refractive index m=n+i k, is an essential parameter when considering the reflection and absorption properties of that material. The refractive index is a function of wavelength of the light, and usually the imaginary part k is what governs the reflection or transmission spectral behavior of the material. The knowledge of the complex refractive index as a function of wavelength, m(λ), is needed for light scattering simulations. On the other hand, rigorous scattering simulations can be used to invert the refractive index from measured or observed reflection spectra. We will show how the combination of geometric optics and radiative transfer codes can be used in this task. In this work, the possible application is with the future visual-near infrared observations of Mercury by the ESA BepiColombo mission. That application in mind, we have used four particulate igneous glassy materials with varying overall albedo and in several size fractions in reflectance spectra measurements (hawaiitic basalt, two gabbronorites, anorthosite, see details from Carli et al, Icarus 266, 2016). The grounded material consist of particle with clear edges and quite flat facets, and we choose to model the particle shapes by geometries resulting from Voronoi division of random seed points in 3D space (see Fig. 1). Figure 1. On the left, a SEM image of anorthosite particles, size fraction 224–250 µm (from Carli et al, Icarus 266, 2016). On the right, eight example particles from Voronoi division algorithm. The refractive index inversion is done here using first a geometric optics code SIRIS (Muinonen et al, JQSRT 110, 2009) to simulate the average Mueller matrix, albedo, and scattering efficiency for a single Voronoi particle. Then, these properties are fed into radiative transfer code RT-CB (Muinonen, Waves in Random Media 14, 2004) to produce the reflective properties of a semi-infinite slab of these particles. This procedure is repeated for a 2D grid of particle size parameters x=2πr/λ, where r is the radius of particle, and imaginary part k of refractive index. In Vis-NIR wavelengths, the real part n is quite constant and is estimated to be about 1.58 for all the four glasses. From the simulated slab reflectance data with the 2D x, k parameter grid, we can first interpolate, and then invert the k parameter for any reflectance value with given wavelength and particle size. The resulting spectral behavior of k for the four glasses and for all the size fractions was seems very realistic. Carli et al. (Icarus 266, 2016) inverted the k spectral behavior for these same samples using Hapke modeling, and the results are quite similar. An example of inverted k for one sample (anorthosite) is shown in Fig. 2. Figure 2. Inverted imaginary part of refractive index, k, as a function of wavelength for different size fractions of anorthosite. We show that rigorous light scattering simulations can be used to invert the optical constant of a material from observed reflectance spectra, at least if some assumptions regarding particle sizes can be done. These methods can be valuable when analyzing various illumination and observing geometries, intimate mixtures of multiple materials, and other cases where Hapke modeling might not be enough for accurate inversion. We foresee employing these methods to analyze the observations of Mercury from ESA BepiColombo mission. Acknowledgements: Research supported, in part, by the Academy of Finland (project 325805).

Asteroids are classified into different taxonomic groups according to their spectral reflectance properties in the visual and near-infrared (Vis-NIR) wavelengths. The spectral properties of the asteroid surfaces can be related to the material of the surface. There are a few taxonomic systems for asteroids, the most recent being the so-called Bus-DeMeo taxonomy (B-DM, DeMeo et al., Icarus 202, 2009). Usually, the exact wavelengths used in the taxonomic system are tied up with the particular survey data that was used to create the taxonomy. With the B-DM taxonomy, it is the SMASSII survey extended to near-infrared with the NASA IRTF telescope observations, and the wavelengths are 0.45–2.45 µm. The ESA space observatory Gaia will produce a significant number of low-resolution asteroid spectra over the 0.33–1.05 µm wavelength range in the Data Release 3 and the final data releases. There is an evident need for evaluating the surface properties of these asteroids using the Gaia data. For example, the list of taxonomic classifications for asteroids, maintained in the NASA Planetary Data System, has 2,600 asteroids with some taxonomic class (Neese, C., Ed., NASA Planetary Data System, 2010), but the Gaia data will eventually contain about 100,000 asteroid spectra. There is a plan to provide a new asteroid taxonomy using the Gaia observations (Delbo et al., PSS 73, 2012). However, a link to existing taxonomic systems such as B-DM would be highly valuable. In this work, we study the possibility to use feed-forward artificial neural network for asteroid spectral classification. We show that the classification accuracy can remain on a reasonably good level even if the B-DM classification is done with the neural network that is trained to use only data having wavelengths in the 0.45–1.05 µm range, which is the overlapping region with the Gaia and the original B-DM systems. This tool can provide the B-DM taxonomic classification for all the asteroids with Gaia spectroscopy. Acknowledgements: Research supported, in part, by the Academy of Finland (project 325805).

We apply the statistical lightcurve inversion method developed by Muinonen et al. (2020, convex inversion in magnitude space CIM) to re-analyze the photometric data of (346) Hermentaria. As a main goal, we compare the results derived by the CIM and original convex inversion method in flux space (CIF) provided by Kaasalainen & Torppa (2001) and Kaasalainen et al. (2001). The comparison concerns the solutions of spin and shape parameters. 1. Introduction The idea to invert 3-D shapes of asteroids from their brightness variations can be traced to 1906 (Russell 1906). Now, several methods have been established to invert the shape of asteroids, the shape models range from triaxial ellipsoids to convex, and even non-convex shapes. Kaasalainen et al. (1992a,b) and Lamberg (1993) suggested a way to invert the convex shape of an asteroid by using the Gaussian surface density. Kaasalainen & Torppa (2001) and Kaasalainen et al. (2001) implemented the idea by the Levenberg-Marquardt algorithm. Now, statistical techniques have been introduced into the photometry inversions of asteroids, e. g., a genetic algorithm (Cellino et al. 2015) and a Markov-chain Monte Carlo approach (MCMC, Muinonen et al. 2015). Wang et al. (2015b,a) presented a virtual observation method to figure out the uncertainties of parameters due to the observational uncertainties. Muinonen et al. (2020) developed a full statistical MCMC algorithm in the convex inversion of asteroids in the magnitude space (CIM), and gives a way to assess the uncertainties of spin parameters and convex shape parameters. We re-analyse the photometric data of (346) Hermentaria with CIM and CIF algorithms, and show the main differences of the results in the derivation of the convex shapes. 2. Convex inversion with Bayesian inference The brightness model used in the CIM (Muninonen et a l. 2020)) involves a convex shape represented with the Gaussian surface density and the Lommel-Seeliger scattering law. In the CIM, the free parameters are the spin parameters, shape parameters, geometric albedo, and two parameters of the H,G1,G2 phase function. As for constructing the convex shape from its Gaussian surface density, Muinonen et al. (2020) developed a computationally easier, stochastic optimization metod. 3. Results and discussion In total, 23 lightcurves of (346) Hermentaria on 4 apparitions are involved. 10 light curves are from the APC database (Lagerkvist et al. 1993) and rest of the lightcurves are ours observations. Based on these data, we performed the shape inversion with the CIM and CIF methods. As only relative intensities are involved, the parameters of the H G1 G2 phase function in the CIM and the scattering parameters a, k,d and c in the CIF are not fitted. Table 1 list the derived spin parameters. Figure 1 shows the lightcurves fits for the case of the pole 2 solution. Table 1. Spin parameters of Hermentaria Method Pole 1 (Ecliptic frame of J2000.0 ) Pole 2 (Ecliptic frame of J2000.0 ) Peroid (h) Pole 1, Pole 2 CIF (133o.0,+17o.2) (319o.5,+16o.8) 17.790043, 17.790039 CIM (133o.8,+09o.6) (321o.9,+17o.2) 17.790016, 17.790097 Figure 1. Lightcurves of Hermentaria (black circles) with the CIM and CIF model intensities ( red crosses and blue pluses respectively). The CIM gives a consistent result on spin parameters. From Figure 1, the modeled lightcurves with the CIF fit well to the features. We think this is partly due to the fact that we use a lower degree of spherical harmonics in the CIM and partly due to the differing model for the observational uncertainties. The theory by Minkowski (1903) provides a way to construct the three-dimensional shape of an object from its Gaussian surface density G. According to Minkowski, Muinonen et al.(2020) developed a stochastic optimization method to construct convex shape. Figure 2 shows the convex shapes of Hermentaria derived by the two methods. Figure 2. Convex shapes of Hermentaria corresponding to Pole 2 solution: the CIM (left) and CIF solutions (right) We have also compared the 3-D shapes constructed by the CIM and the CIF using the same Gaussian surface density originally derived by the CIM. Figure 3 shows the CIM and CIF results and by visual inspection, the results are very close to one another. Figure 3 Convex shapes of Hermentaria corresponding to the same Gaussian surface density: the CIF (left) and CIM reconstructions (right). 4. Summary We applied the statistical convex inversion method (Muninonen et al. 2020) to analyze the photometric data of Hermentaria. The best-fit solution of the spin parameters and shape as well as the uncertainties of the estimated parameters can be derived. We compared the results to that of the CIF and found that the spin parameters are consistent with one another. The Gaussian surface density derived by the two methods is slightly different which leads to slightly different convex shapes. For validating the new shape reconstruction method in Muinonen et al. (2020), we compared the shape derived by the methods of Kaasalainen tel al.(2001) and Muinonen et al. (2020) from the same Gaussian surface density, and found them to be similar. References Cellino, A., Hestroffer, D., Tanga, P., Mottola, S., & Dell’Oro, A. 2009, A&A, 506, 935 Cellino, A., Muinonen, K., Hestroffer, D., & Carbognani, A. 2015, PSS, 118, 221 Kaasalainen, M., Lamberg, L., & Lumme, K. 1992a, A&A, 259, 333 Kaasalainen, M., Lamberg, L., Lumme, K., & Bowell, E. 1992b, A&A, 259, 318 Kaasalainen, M. & Torppa, J. 2001a, Icarus, 153, 24 Kaasalainen, M., Torppa, J., & Muinonen, K. 2001b, Icarus, 153, 37 Lagerkvist, C.-I., Erikson, A., Debehogne, H., et al. 1995, A&A Supplement Series, 113, 115 Lamberg, L. 1993, Ph.D. thesis, University of Helsinki, Finland, vol. 315L Lumme, K. & Bowell, E. 1981, Astron J, 86, 1694 Minkowski, H. 1903, Mathematische Annalen, 57, 447 Muinonen, K. & Lumme, K. 2015a, A&A, 584, A23 Muinonen, K., Wilkman, O., Cellino, A., Wang, X., & Wang, Y. 2015b, PSS, 118, 227 Muinonen ,K., Torppa, J., Wang, X.-B., Cellino,A., Penttilä , A., 2020, submited to A&A, in revised Russell, H. N. 1906, Astrophys J, 24, 1 Wang, X., Muinonen, K., & Wang, Y. 2015a, PSS, 118, 242 Wang, X., Muinonen, K., Wang, Y., et al. 2015b, A&A, 581, A55

Light scattering from self-affine homogeneous isotropic random rough surfaces is studied using the ray-optics approximation. Numerical methods are developed to accelerate the first-order scattering simulations from surfaces represented as single-connected single-valued random fields, and to store the results of the simulations into a numerical reflectance model. Horizon mapping and marching methods are developed to accelerate the simulation. Emphasis is given to the geometric shadowing and masking effects as a function of surface roughness, especially, to the azimuthal rough-surface shadowing effect., Published in JQSRT 106 (2007)

The spherical wavelet based on the lifting scheme is introduced for adaptive discrete-ordinate sampling of the radiation fields, particularly, in the radiative transfer computation using iterative schemes. The lifting scheme for wavelet transform is described from an implementation point of view, including the construction of hierarchical geodesic grids on the sphere and wavelet constructions. In addition, we compare the method with the conventional spherical harmonics, numerically investigating the transformation error and efficiency. The transformation matrices are built in the least-squares sense. The results demonstrate the feasibility of using spherical wavelets as an adaptive discrete-ordinate sampling method at the cost of O(N), where N is the number of significant coefficients.

We analyze spectrophotometric observations of Mercury acquired from the Mercury Dual Imaging System (MDIS) on board NASA’s MErcury Surface, Space Environment, Geochemistry and Ranging mission’s spacecraft (MESSENGER). The spectrophotometric properties provide insight into regolith composition and structure, which in turn provide insight into surface processing. Using the Lommel-Seeliger reflection coefficient, we derive first estimates for the single-scattering phase function and the disk-integrated phase curve in eight colors. The results help us prepare for the interpretation of the Mercury observations by the ESA/JAXA BepiColombo mission. 1. Introduction Planet Mercury continues to challenge scientific interpretation. Mercury’s principal rotational characteristics were unveiled only in 1960’s and its surface composition remains largely open. The elemental chemistry instruments on board the MESSENGER spacecraft provided constraints on many elements [1-6], however the surface mineral composition remains a mystery [7]. Mercury will soon be scrutinized by the BepiColombo mission that will examine the surface over a broader range of wavelengths, promising to identify the mineral composition. Spectrophotometry provides constraints on the physical and chemical properties of the regolith (e.g., [8]). We analyze MDIS eight-color disk-resolved photometry with the Lommel-Seeliger reflection coefficient (LS), the simplest model valid for regoliths with dark constituent materials. The LS coefficient has been recently utilized in, e.g., asteroid lightcurve inversion using disk-integrated photometry from the ESA Gaia mission [9]. The Gaia photometry unveils asteroid phase curve slopes in the phase-angle range of 15-35o. Examination of the Mercury photometry using the LS coefficient allows for the determination of the single-scattering phase function over MDIS’ wavelength range, paving the way for the assessment of BepiColombo Mercury data [10,11]. 2. Modeling, results, and discussion We make use of the LS reflection coefficient with the single-scattering phase function as in [9]. The disk-integrated phase function is introduced as part of the single-scattering phase function using a divisor that corresponds to the disk-integrated phase function for isotropic scattering. It follows that the data points themselves suggest the shape of the phase functions. Figure 1 shows the single-scattering phase functions as point clouds when reduced from the full MDIS data set (e.g., [8]). The filter wavelengths are as follows (in nm): λ(F)=433.2, λ(C)=479.9, λ(D)=558.9, λ(E)=628.8, λ(G)=748.7, λ(L)=828.4, λ(J)=898.8, λ(I)=996.2. In order to minimize surface roughness effects, we have required that the incidence angle is less than 40o. Figure 1: Single-scattering phase functions as indicated by the processed data points. In Figure 2, we show the disk-integrated phase curves. The phase curves look realistic for phase angles o, whereas, for phase angles >60o, there is a bump that can be due to the simplicity of the LS coefficient. Figure 2: Disk-integrated phase curve as indicated by the processed data points. Figure 3 shows linear magnitude-scale fits to the data, with normalization to zero magnitude at 30o phase angle, when both incidence and emergence angles are required to be less than 40o. Color dependence is evident and there are indications of reddening as a function of phase angle. Although exceptions are present, the slopes tend to become shallower with increasing wavelength, in agreement with the increasing reflectance of Mercury with wavelength [12]. Figure 3: Linear fits to the single-scattering phase function data for incidence and emergence angles o. 3. Conclusion We have carried out a preliminary analysis of the MESSENGER observations. By concentrating on data at small incidence and emergence angles, we obtain realistic first estimates for the single-scattering phase function. This, in turn, allows us to estimate the disk-integrated phase curve of Mercury. We detect reddening with the phase angle and flattening with increasing spectral reflectance. The features relate to the properties of regolith particles. We will continue the analysis by accounting for surface roughness and porosity (e.g., [13]) and recent advances in space weathering modeling [14,15]. Acknowledgments. Research by KM, VB, and AP supported, in part, by the Academy of Finland (grant 325805). DD is supported by NASA's Solar System Working program (grant 80NSSC18K0521). References [1] Nittler, L. R., et al.: The major-element composition of Mercury’s surface from MESSENGER X-ray spectrometry, Science, Vol. 333, pp. 1847–1850, 2011. [2] Peplowski, P. N., et al.: Enhanced sodium abundance in Mercury's north polar region revealed by the MESSENGER Gamma-Ray Spectrometer, Icarus, Vol. 228, pp. 86-95, 2014. [3] Peplowski, P. N., et al.: Radioactive elements on Mercury’s surface from MESSENGER: Implications for the planet’s formation and evolution, Science, Vol. 333, pp. 1850–1852, 2011. [4] Peplowski, P. N., et al.: Variations in the abundances of potassium and thorium on the surface of Mercury: Results from the MESSENGER Gamma-Ray Spectrometer, J. Geophys. Res., Vol. 117, E00L04, 2012. [5] Weider, S. Z., et al.: Chemical heterogeneity on Mercury’s surface revealed by the MESSENGER X-Ray Spectrometer, J. Geophys. Res., Vol. 117, E00L05, 2012. [6] Evans, L. G., et al.: Major-element abundances on the surface of Mercury: Results from the MESSENGER Gamma-Ray Spectrometer, J. Geophys. Res., Vol. 117, E00L07, 2012. [7] Izenberg, N. R., et al.: The low-iron, reduced surface of Mercury as seen in spectral reflectance by MESSENGER, Icarus, Vol 228, pp. 364–374, 2014. [8] Domingue, D. L., et al.: Application of multiple photometric models to disk-resolved measurements of Mercury’s surface: Insights into Mercury’s regolith characteristics, Icarus, Vol. 268, pp. 172-203, 2016. [9] Muinonen, K., et al.: Asteroid lightcurve inversion with Bayesian inference, Astronomy & Astrophysics, in revision, 18 p., 2020. [10] Cremonese, G., et al.: SIMBIO-SYS: Scientific cameas and spectrometer for the BepiColombo mission, Vol. 216, 75, pp. 1-78, 2020. [11] Rothery, D., et al.: Rationale for BepiColombo studies of Mercury’s surface and composition, Space Science Reviews, Vol. 216, 66, pp. 1-46, 2020. [12] McClintock, W. E., et al.: Spectroscopic observations of Mercury’s surface reflectance during MESSENGER’s first Mercury flyby, Science, Vol. 321, pp. 62-65, 2008. [13] Wilkman, O., et al.: Photometry of dark atmosphereless planetary bodies: an efficient numerical model, Planetary and Space Science, Vol. 118, pp. 250-255, 2015. [14] Penttilä, A., et al.: Rigorous light-scattering simulations of space-weathering effects on reflectance spectra. Icarus, Vol. 345, 113727, pp. 1-8, 2019. [15] Muinonen, K., et al.: Scattering and absorption of light in planetary regoliths. J. Visual. Exper., Vol 149, e59607, doi:10.3791/59607, 2019.

Asteroids have remained mostly the same for the past 4.5 billion years, and provide us information on the origin, evolution and current state of the Solar System. For the physical characterization of asteroids, one of the best data sources is photometry: the measurement of the disk-integrated brightness of the asteroid. An asteroid's lightcurve (i.e. the dependency of the brightness as a function of time) is indicative of its surface scattering properties, as well as its shape and the state of spin. In this work, we apply novel Bayesian inverse methods (Muinonen et al., A&A 2020, in revision) to derive phase curve parameters from photometric lightcurve observations. Our aim is to validate and expand the existing analyses by applying the methods to of the order of tens to hundreds of asteroids using photometric data from the Gaia Data Release 2 (Gaia Collaboration, Spoto et al., A&A 616, A13, 2018) and ground-based photometry (Durech et al., A&A 513, A46, 2010) from Database of Asteroid Models from Inversion Techniques (DAMIT). We derive phase curve linear slopes by using four techniques: 1) convex inversion on all data, 2) convex inversion on all data with fixed rotation parameters from DAMIT, 3) ellipsoid inversion on Gaia DR2 data only, and 4) ellipsoid inversion on Gaia DR2 data only with fixed rotation parameters from DAMIT. Finally, we compare the obtained slope parameters with the presumed Bus-DeMeo (DeMeo et al., Icarus 202, 160, 2009) taxonomic classes of the asteroids, and study possible correlations with the geometric albedos. The Gaia photometry has milli-magnitude precision and is thus extremely valuable when used to carry out asteroid taxonomic classification.

We are compiling a service, which will produce almost real-time estimates of the Earth Bond albedo in visual and near-infrared wavelengths using the multi-wavelength images from the NOAA Deep Space Climate Observatory’s (DSCOVR) Earth Polychromatic Imaging Camera (EPIC). The service will be based on the known land and sea surface types of the Earth and the angular distribution models (ADMs) from the Clouds and the Earth’s Radiant Energy System (CERES) project (some details in Ihalainen, M.Sc. thesis, 2019, University of Helsinki, Finland). Instead of applying the CERES ADM albedo estimates as such, we will only use the ADM shapes for different land and sea surface types, but scale them using the corresponding observations from the EPIC camera. As the EPIC camera will produce imaging of the Earth disk from the L1 point, in about every two hours and in 10 narrow band filters between 317–780 nm, we can follow the temporal changes in the Bond albedo both in short times scales and over longer periods. We will employ a custom-made classifier for cloud coverage over the Earth disk using the 10 bands in the EPIC images to improve the Bond albedo estimation with temporally suitable cloud coverage ADMs over the land or sea surface pixels. The service will be run automatically in a dedicated server, and will produce the Bond albedo estimates via a public web interface. Figure 1. An example image from EPIC camera, taken at Jan. 1st, 2019. The three first images, counting from the top left corner, are gray-scale images at wavelength bands 317 nm, 388 nm, and 780 nm. The fourth image is false-color RGB composite from those channels. Acknowledgements: Research supported by the Academy of Finland (project 298137).

The optical properties of a sample are important in, e.g., astrophysics and space science. The samples can be unique or available in limited quantities, implying that sample preservation is important. Established single-particle light-scattering measurements involve attaching the sample to a holder or measuring a laminar flow of particles, neither of which allows for a controlled and non-destructive measurement. Acoustic levitation is a state-of-the-art approach applicable to scattering measurements. We present an instrument capable of performing a full 4π scattering measurement, i.e., a measurement from any direction on the full 4π solid angle. We measure scattering properties of millimeter-sized samples at any direction. This is enabled by introducing a novel non-contacting sample holder based on acoustic levitation, which allows a disturbance-free measurement of an orientation-controlled sample. The instrument is scalable and currently employs polarized visible light (400–700 nm). It also measures beam and sample stability as well as temperature and humidity, to ensure consistency of measurements. We demonstrate a measurement of a sample consisting of agglomerated 500-nm silica spheres. The upper left 2×2 submatrix of the Mueller scattering matrix is measured from the sample along the scattering angle. 1. Introduction Experimental measurements of light scattering by a small-particle sample in a controlled position and orientation (six degrees of freedom) has remained open. Scattering characteristics for single particles have been earlier measured as ensemble averages over the size, shape, and orientation distribution (e.g., [1]) by introducing a particle flow through the measurement volume. Scattering characteristics for single particles in levitation have been carried out using, for example, electrodynamic levitation [2] and optical tweezers [3-5]. In the present manuscript, a novel experimental method based on ultrasonic levitation with full control of the sample position and orientation is offered [6-8]. 2. Levitator-scatterometer: results and discussion Figure 1 shows our levitator scatterometer with detailed information about its components. Figure 1: Levitator-scatterometer with a photograph (above) and top view schematic (below). The components are as follows: (1) fiber-coupled light source with collimator, (2) focusing lens (optional), (3) bandpass filter for wavelength selection, (4) adjustable aperture for beam shaping, (5) motorized linear polarizer, (6) high-speed camera, (7) high-magnification objective, (8) acoustic levitator for sample trapping, (9) measurement head, comprising an IR filter, motorized shutter, motorized linear polarizer, and a photomultiplier tube (PMT), (10) motorized rotation stage for adjusting measurement head angle, (11) optical flat for Fresnel reflection, (12) neutral density filter, and (13) reference PMT, for monitoring beam intensity. The system is divided into three enclosed compartments to eliminate stray light. For the experiment, an aggregate consisting of densely-packed, nominally 0.5-µm diameter spherical SiO2 particles was selected and polished further, to approximate a spherical shape, after which it was characterized by weighing and measuring its dimensions (Fig. 2). The nearly spherical aggregate had a diameter of 1.16 mm and a volume density of 0.47. The light beam was filtered to 488±5 nm, with a Gaussian spectrum. The measured phase function, degree of linear polarization for unpolarized incident light, as well as the depolarization are shown in Figs. 3-5, respectively, as a function of the phase angle (source-sample-detector angle). Figure 2: The sample of densely-packed spherical SiO2 grains. Figure 3: The measured and modeled phase functions normalized to unity when integrated from 15.1° to 165.04°. Figure 4: Degree of linear polarization for unpolarized incident light (Mueller scattering-matrix-element ratio -M12/M11 in %) from the measuements and modeling. Figure 5: Depolarization (M22/M11) from the measurements and modeling. Figures 3-5 further include the first modeling based on the R2T2 and SIRIS4 software (Radiative Transfer with Reciprocal Transactions; see [6] and references therein). The phase function is accurately modeled, whereas there are challenges remaining for modeling the degree of polarization and depolarization. There is compelling need for high-precision validation samples with accurate documentation: the size and shape distributions of the silica samples remain too uncertain to be utilized in model validation. Conclusion We have described novel experimental instrumentation for measuring light scattering by isolated samples in levitation. As it is extremely difficult to accurately characterize random media composed of sub-wavelength-scale particles or inhomogeneities, controlled Mueller-matrix measurements can offer a tool for retrieving information on the volume density and particle size and shape distribution in the medium. Acknowledgments. Research by KM, AP, HH, and MG supported, in part, by the Academy of Finland (grants 325805 and 325806). References [1] Muñoz, O., Volten, H., de Haan, J. F., Vassen, W., and Hovenier, J. W.: Experimental determination of scattering matrices of olivine and Allende meteorite particles, Astron. Astrophys., Vol. 360, pp. 777–788, 2000. [2] Sasse, C., Muinonen, K., Piironen, J., and Dröse, G.: Albedo measurements on single particles, J. Quantitat. Spectrosc. Radiat. Transf., Vol. 55, pp. 673—681, 1996. [3] Gong, Z., Pan, Y.-L., Videen, G., and Wang, C.: Optical trapping and manipulation of single particles in air: Principles, technical details, and applications, J. Quantitat. Spectrosc. Radiat. Transf., Vol. 214, pp. 94–119, 2018. [4] Nieminen, T. A., du Preez-Wilkinson, N., Stilgoe, A. B., Loke, V. L. Y., Bui, A. A. M., and Rubinsztein-Dunlop, H. Optical tweezers: Theory and modelling. J. Quantitat. Spectrosc. Radiat. Transf., Vol. 146, pp. 59–80, 2014. [5] Herranen, J., Markkanen, J., and Muinonen, K. Dynamics of interstellar dust particles in electromagnetic radiation fields: A numerical solution. Radio Sci., Vol. 52(8), pp. 1016–1029, 2017. [6] Muinonen, K., Väisänen, T., Martikainen, J., Markkanen, J., Penttilä, A., Gritsevich, M., Peltoniemi, J., Blum, J., Herranen, J., Videen, G., Maconi, G., Helander, P., Salmi, A., Kassamakov, I., and Haeggström, E.: Scattering and absorption of light in planetary regoliths. J. Visual. Exper., Vol. 149, e59607, doi:10.3791/59607, 2019. [7] Maconi, G., Helander, P., Gritsevich, M., Salmi, A., Penttilä, A., Kassamakov, I., Haeggström, E., and Muinonen, K.: 4π scatterometer, J. Quantitat. Spectrosc. Radiat. Transf., Vol. 246, 106910, 1-7, 2020. [8] Helander, P., Puranen, T., Meriläinen, A., Maconi, G., Penttilä, A., Gritsevich, M., Kassamakov, I., Salmi, A., Muinonen, K., and Haeggström, E.: Omnidirectional microscopy by ultrasonic sample control, Appl. Phys. Lett., Vol. 116, 194101, 1-5, 2020.